Question 397870
I did the following problem, but I am not certain I did it correctly. I am hoping a tutor can double check this for me, and put me on the right path if it is wrong. Any help would be greatly appreciated! Here is the problem:

Find f^-1(x) 

f(x)= (2x-3)/(x+1)

Here's how I did it:

f(x)=2x-3/(x+1)

y=2x-3/(x+1)

x=(2y-3)/(y+1)

xy= (2y-3)/(y+1)*y

xy= 2y-3 ******   That won't work.

xy-2y=-3

y(x-2)/(x-2)=-3/(x-2)

y=-3/(x-2)

so f^-1(x)= -3/(x-2)

Ok...Is this correct, or do I need to go back to the drawing board? Could someone please show me how to check these? Thank you!
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x=(2y-3)/(y+1)
x(y+1) = 2y-3
xy+x = 2y-3
xy - 2y = -x-3
y(x-2) = -x-3
y = (-x-3)/(x-2)
y = -(x+3)/(x-2)